Abstract
This paper studies the preview tracking control problem for linear discrete-time periodic switched systems. Firstly, an augmented error system is constructed for each subsystem by stabilizing the augmented error systems through the method of optimal preview control, and the tracking problem of the switched system is transformed into the switched stability problem of closed-loop augmented error systems. Secondly, a switched Lyapunov function method is applied to search the minimal dwell time satisfying the switched stability of the closed-loop augmented error systems. Thirdly, the switched preview control input is solved from the controller of the individual augmented error system, and then the sufficient conditions and the preview controller can be obtained to guarantee the solvability of the original periodic switched preview tracking problem. Finally, numerical simulations show the effectiveness of the stabilization design method.
Highlights
Switched system theories are a hot topic of control theory research in recent years [1,2,3,4,5]
An augmented error system is constructed for each subsystem by stabilizing the augmented error systems through the method of optimal preview control, and the tracking problem of the switched system is transformed into the switched stability problem of closed-loop augmented error systems
A switched Lyapunov function method is applied to search the minimal dwell time satisfying the switched stability of the closed-loop augmented error systems. irdly, the switched preview control input is solved from the controller of the individual augmented error system, and the sufficient conditions and the preview controller can be obtained to guarantee the solvability of the original periodic switched preview tracking problem
Summary
Switched system theories are a hot topic of control theory research in recent years [1,2,3,4,5]. En, according to the optimal control theory, the controller of the switched augmented error systems is obtained, and the sufficient condition for the global asymptotic stability of closed-loop systems is given. To avoid the difference operation for the whole switched systems and include the previewable information in the controller, an augmented error system is constructed for each subsystem, which successfully converts the original problem into the asymptotical stability problem for the switched closed-loop augmented error subsystems. (2) e dwell-time condition, which heavily depends on the stable coefficient matrices of the closed-loop augmented error subsystems, is obtained to ensure the asymptotical stability of the switched closed-loop augmented error systems and the solvability of the preview tracking problem for switched systems. Notations. roughout this paper, A > 0 indicates that A is a positive definite matrix, rank(A) denotes the rank of A, x ∈ Rn means that x is an n-dimensional vector, A ∈ Rn×r means that A is a real matrix of n × r, ‖x‖ denotes the Euclid norm for vector x, ‖A‖ denotes the matrix norm derived from the vector Euclid norm, and max{a, b} means the maximum value between a and b
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